The insulating state of matter: a geometrical theory

Abstract.

In 1964 Kohn published the milestone paper “Theory of the insulating state”, according
to which insulators and metals differ in their ground state. Even before the system is excited
by any probe, a different organization of the electrons is present in the ground state and this is
the key feature discriminating between insulators and metals. However,
the theory of the insulating state remained somewhat incomplete until the late 1990s; this review addresses the recent
developments. The many-body ground wavefunction of any insulator is characterized by means of
geometrical concepts (Berry phase, connection, curvature, Chern number, quantum metric). Among
them, it is the quantum metric which sharply characterizes the insulating state of matter. The
theory deals on a common ground with several kinds of insulators: band insulators, Mott insulators,
Anderson insulators, quantum Hall insulators, Chern and topological insulators.

Keywords

Topological Insulator Berry Phase Resta Chern Number Wannier Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.